Seismic exploration by means of periodic excitation



Sept. 5, 1950 s. A. SCHERBATSKOY 2,521,130

SEISMIC EXPLORATION BY MEANS OF PERIQDIC EXCITATION Filed June 10, 19452 Sheet-Sheet 1 FILTER METER AMPLIFIER 7 I7 V V K EARTH SURFACE-OSCILLATOR 2/0 DIFFERENTIAL GEAR FIG. 4

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/N I/E N TOR Sept. 5, 1950 s. A. SCHERBATSKOY SEISMIC EXPLORATION BYMEANS OF PERIODIC EXCITATION Filed June 10, 1943 2 Sheets-Sheet 2 am mmmmnEOUum 3 e vw 254mm Patented Sept. 5, 1950 UNITED STATES SEISMICEXPLORATION BY'MEANS or PERIODIC nxcrcrarron Serge Al Scherhatskoy',mascara- Application June 10, 1943,'Seria};No; 4 E374 l My inventionrelates to seismic prospecting systems and more particularly to systemsused for seismological exploration and provides a new and improvedmethod for receiving and recording seismic vibrations and the like.

i Seismological exploration consists in surveying the geologicalstructure of the subsurface and determining the depths and slopes ofsubsurface strata with a view towards locating formations iavorable tothe accumulation of oil and other valuable minerals.

'One of the methods of determining the subsurface strata comprisescreating earth vibrations by detonating an explosive at or near thesurface of the earth and producing seismograms, i. e, graphical recordsof vibrations after they 8 Claims. (Cl.

have been influenced by various geological strata and returned to thesurface of the earth. These records are used thereafter to furnishdatafrom which the geological structure may be deduced and plotted. Thismethod has been designated as the method of seismic prospecting bytransient excitation and consists essentially in determining the timeinterval required for a shock originating with the explosion of aquantity of dynamite to reach a distant point. In the seismic method bytransient excitation, frequency does not enter into calculations and itenters only as regards the selective treatment by the receivingapparatus and some earth materials, since some frequencies are amplifiedmore than others in the receiving apparatus and some are absorbed orselectively reflected or refracted by certain earth materials.

Another method of determining subsurface strata has been suggested inthe past and designated as the seismic prospecting method by continuousexcitation. In this method the seismic waves are generated by continuousand periodic excitation and the behavior of the earth is studied inrelation to the frequency oi the excited seismic waves. Certaincharacteristic frequencies corresponding to resonant conditions of theearth are obtained, and yield important information regarding thegeological structure to be determined.

The present invention relates to the seismic prospecting methods bycontinuous excitation. In these methods seismic waves oi varyingfrequencies are being imparted to the earth, and the correspondingmotion of the earths surface is being recorded at. a distant point. Oneof the methods of seismic prospecting by continuous excitation has beendescribed in the U. S. Patent 1,790,080, issued on January 27, 1931, toA. N. Stanton.

It is a parent tnat in all measurements involved in themethod'bf'seismic prospecting by contin'ucus' v excitation certainrequirements as to niea'surability of the signal received have to befulfilled Among these requirements. is a satisfactorysig'nal to'noi'seratio. The signalhere is representedby'the various waves that arebrought into being" as a result of the periodic excitation of theearthmeans of a vibrator, and by noise is meant What'is usually referredto as micro sjeismsf f These microseisms are produced by causes ofvarious'origins and these origins include effects of ocean waves on thesurface, efi'ects of temperature changes in the earth, effects Icaused'by wind on various objects on the earth, effectsdu'e to themotion of rivers in the neigh boring egio s and; also to some extentvibrations 'lcausedby a ma; life. A great amount of study has'bee'ndevoted to microseisms and it has been established that at least in theregion of frequen cies that'are used in seismic exploration the fre tue'ncie's or tnmicroseims are" arranged in a con- 'tinuous spectrum; i.e1, all frequencies within a certain range. are represented.Micros'ei'sms are somewhat-similar "to electrical thermal noises causedby" thermalexcitation in electrical con ductors, and effects known asBrownian motions, and to effectsfthat are encountered in radiation,mea'surementsdue to the'quantized propagation of radiations. In allthese effects the energy representing the phenomena being considered is.distributed'oyer a wide range of frequencies and the power representedby any single discrete fre-' quency is zero; The effective power isentirely dependent spaa. band'filter' to which the Incasiuring'apparatus is responsive and in the case of strictl uniform distributedenergy as in" 616G?- trical thermal noise the power decreases directlywith the width of thej band.

In the prior methods of seismic prospecting in which a transient impulsewas generated in the earth by means of a dynamite explosion it wasnecessary to. produce a signal. wave corresponding to a reflected 'or'arefracted wave havingian amhas to be applied to the earth. It is wellknown that the process, of exploding dynamite inorder .to "produc'e'anearth vibration is very inenicfent and a great amount ofheat isgenerated and that various other violent disturbances resulting inpermanent deformation of the earth in the ViCiIl-r ity of the" dynamiteexplosion do not contribute efficiently to the propagation of theelastic waves in the earth. Recently more efficient processes forimparting seismic energy into the ground have been tried as for exampleby means of an arrangement described in the U. S. Patent 2,203,140,issued June 4, 1940, to W. G. Green. By means of these processes goodresults have been obtained with only foot tons of energy and it can beassumed that this figure could be reduced somewhat further by efficientdesign of the apparatus for initiating the elastic waves in the earth.

It is apparent that in the seismic method by periodic excitation, eachindependent measurement is a measurement of the amplitude of a singlediscrete frequency and that if sufficient time is available to performthe measurement of the amplitude of this discrete frequency, the bandwidth to which the measuring apparatus responds can be reduced almostindefinitely. Taking as a starting point a measuring apparatus of theconventional type that responds to a. band width of 100 cycles, it hasbeen found that the amount of energy that is required is of the order of10 foot tons. It is obvious that if for example the band width of theappara- .tvs is reduced to 1 cycle per second, the amount of energyrequired would be only one foot ton. Furthermore, if the band width wereto be reduced to .01 cycle per second the amount of power required wouldbe only foot ton.

Heretofore one of the very important problems which have been incapableof solution was the design of a generator that would impress upon theearth a periodic excitation having sufliciently large energy to producea, reflected or refracted wave at the receiving instrument that wouldoverride the noise by a sufficient margin. Very large vibratorsobviously could be constructed but they would be extremely cumbersomeand expensive to use and so far this has been found to be impracticaland no industrial work has been done in connection with exploration forpetroleum in which the periodic excitation was used. j vIt is an objectof my invention to provide a detecting apparatus that is many times moresensitive than previously used for detecting the incoming waves and thatwill permit the use of a generator that is many times smaller than theprevious ones used in order to accomplish this increase in sensitivity.It is necessary that the instrument be provided with an extremely sharpfilter having a band width of the order of ,4 of a cycle per second andit is further necessary ,to' provide a convenient means for shifting themid-frequency of this band width so as to make it follow exactly thevarying frequency of the generator that imparts the vibrations to theearth.

The general arrangement and further objects of my invention will be moreclearly understood ..with reference to the drawings in which:

Fig. 1 illustrates schematically an arrangement for generating andreceiving seismic waves in accordance with my invention.

gram of the received seismic waves obtained by means of the arrangementof Fig. 2.

Fig. 4 shows a modified fragment of Fig. 2 in which the phase controlbetween two electrical currents is performed manually.

Fig. 5 gives a schematic diagram of a double balanced modulator.

Referring now more particularly to Figure 1 there is showndiagrammatically the working principle of my invention. Numeral Itindicates a vibrator adapted to vibrate the earth. The frequencyof thevibrator is capable of continuously varying as designated symbolicallyby means of an arrow II. This generator therefore excites the earth andsends out elastic waves. Numeral I2 is a geophone adapted to pick up theearth vibrations. Numeral I3 is an extremely sharp band pass filter themid-frequency of which can be varied as designated symbolically by meansof an arrow [4. An arrangement is provided to cause this frequency tofollow exactly the frequency of generator I 0 as designated symbolicallyby means of a line l5 connecting the arrows H and I4. Numeral l6designates a vacuum tube amplifier and numeral i1 dsignates a meteradapted to indicate the output of the filter i3. If the-frequency of thegenerator |0--is varied then the mid-frequency of the filter I3 is madeto follow the frequency variation of the generator and, consequently,the signal to noise ratio capable of being produced by the detectingapparatus is very large and is dependent primarily upon the width of theband to which the system as a whole is responsive. The filter 13 that Ipropose to use is only a small fraction of a cycle wide and very goodsignal to noise ratio can be produced and transmitted to the meter l'l.

Figure 2 shows a detailed representation of an arrangement similar tothe one shown in Figure 1. Referring now more particularly to Fig. 2,numeral 20 indicates an oscillator which is of the conventional vacuumtube type, the frequency of which can be varied by means of a suitablecontrol element such as a condenser 2|. The condenser 2| is adapted tobe driven by a Selsyn motor 22, the said motor 22 being in synchronousconnection with a manually'driven Se1syn motor 23. The Selsyn motor 23is made to turn by means of a handle 24 in a manner such that theangular position of the handle 24 at all times corresponds to a definiteangular position of the condenser shaft 25 of the condenser 2| and,consequently, to each angular position of the handle 24 therecorresponds a definite frequency of the oscillator 20. The oscillator 20is connected to a synchronous motor 26 and this motor consequentlyrotates at a rate that is determined by the frequency of the oscillator20. The motor 26 by means of shaft?! drives an eccentric type earthvibrator 28. Such earth vibrators have been described in the past byother workers and no detailed description is required here. It issufficient to say that this vibrator may comprise a large flywheel 30half'of which is removed, this flywheel being mounted upon a suitablesupport 3|. The earth vibrator that I am using in the present embodimentmay be substantially similar to the one described in the U. S. Patent1,790,080, issued on Jan. 27, 1931, to Austin N. Stanton. It is apparentthat the unbalanced wheel when driven at a high rate of speed produces avarying pressure on the surface of the ground and thus generatesvibrational waves in the ground. The synchronous motor 26 also drives bymeans of a shaft 32 a differential gear 34, the said differential gearbeing connected by means of a shaft 36 to a generator 38. Thesynchronous motor 26 and the generator 38 are of an identicalconstruction, and, therefore, if they are synchronously run, the voltageinput of the synchronous motor *26 is of-the samerreoueaey as thevoltage output of the generator-38, the phase difierenee between saidinput and output being dependent upon the relative angular displacementof the rotors of the motor 28 and the generator 38 respectively.Consequently, the generator 38 generates a voltage across the loads 40which at all times has exactly-the same frequency as the voltagesupplied byth oscillator 2-8 but has a phase that can be shiftedcontinuously with respect to the voltage of the oscillator 20 by meansof the differential gear 3 5. The third shaft 62 of the differentialgear 34 is connectedto a small slow speed D. 0. motor 45 the armature ofwhich is designated as it and isenergized from a conventional source ofpower asfor example the battery 41 and the field winding 38 of which isadapted to external excitation. The motor 35 is adapted by means of theshaft %2-too0ntrolthe difierential gear E i and in such a manner tocontrol the relative phase position of the rotors oi the synchronousmotor 26 and of the generator 38. When the shaft 42 is stationary, theshafts 32 and 35 of the difierential gear rotate in opposite directions,but at exactly the same number of revolutions per second. Whenever theshaft 42 is made to rotate slowly by means of the motor 35, the shaft 35is made to slowly advance or retard with respect to shaft 32 in a mannersuch that the first position of the rotor of the motor 26 can be made togradually advance or fall behind the first position of the rotor of thegenera tor 38.

It is apparent that the control of the motor 35 and, consequently, thecontrol of the phase between the input voltage of the motor 25 and theoutput voltage of the generator 33 can be effected by means of thevoltage applied across the excitation winding 48 of the motor 45. For example, if the polarity of the voltage applied across the loads 55, 5!connected to the terminals of the winding 68 is such, that the lead 50is made to be electrically positive with respect to the lead 55, themotor 45 will rotate in a given direction and introduce an advance inphase of the'rotor of s the generator 33 with respect to the rotor ofthe motor 25. Conversely, as the lead 563 is made negative with respectto the lead 5! the motorAB will rotate in the opposite direction andwill introduce a retardation in phase of the rotor of the generator 38with respect to the rotor of the motor 26.

A geophone 613 is located at a distance chfrom the earth vibrator 23 andis set into a continually vibratory motion by the various Waves'thatarrive at the geophone to from the vibrator 28 through several pathsthat shall be described hereafter. The geophone output is subsequentlyamplified in the amplifier ill. The output terminals of the amplifier t!are connected directly to a balanced modulator t2 and are also connectedto the input terminals of a derivator 63, the output terminals of saidderivator being connected to a balanced modulator 65. The derivator 63consists of a circuit that is adapted to produce at its output anelectrical voltage the instantaneous value of which is proportional tothe first time derivative of the voltage at its input. The exactbehavior of the circuit of this type is well known in the art and itsdescription can be found in the U. S. Patent 2,099,536 issued on June11, 1940, to S. A. Scherbatskoy and J. Neufeld wherein a derivatorcircuit is illustrated in Fig. 4a.

Balanced modulators designated by the blocks 62 and 65 are well known inthe art and have been described ih a'n article by R. 'S. oarruthers onC'opper' QXide Modulators in Carrier."Tele phone Systems, The BellsystemaTechnical Journal, vol. XVIII, 1939-, pp;- ':315337. :,The typeof the circuit containedin; rectangles 2. and 65 is illustrated inFig.-2c-page 318- 0f the said article andis also designated as a ringmodulator ora double balanced'modulator. By 7 double balanced is meant amodulator in whi'eh each input is balanced out from theoutput, and theoutput contains therefore substantially only the modulation products.The structural-and operative "characteristics of a double balancedmodulator will be explained more in detail in connection with Figured vA l The modulators 62 and 65 are adapted. to pro duce attheiroutputsvoltages that are equal to the products of the voltagesimpressedat their inputs. As shown in the-figure, the-modulator 65 hasone pair'of its input terminals designatedby 10 connected to the outputof the derivator 63 and the other .pair of its input terminals,designated by H connected to the output ofthe generator 38 by means ofloads 40. Therefore; the modulator 65 produces across its outputterminals-15d; 15b modulation "products of Volta'ges derived from thederivator lit and the gen; erator- 38. In a similar manner; themodulator 62 has ohepa'ir of its inputfterrninals, designated by 18connected tothe output ('if tlie' amplifier 6i and the other pair'ofitsinput-terminals, desig nated byconnected to the eutput-of-the'geneerator 38 by means of leads 40. Thereiorejthe modulator EZ-producesacross its output renalnals 82 modulation products of voltages derivedfrom the amplifier 8i and thegenera'to'r38. The" outputs of themodulators 62,155 are respectively connected to low pass filters 89990which are adapted to pass only extremely low-frequencies; i; e.,frequenciesr-angingfrom-zero up to a small fraction of-acycle.

The output of the filter 9B is connected-to photographic recordercontained within a (kitted rectangle Bland comprising a-photosensitivestrip of paper 9 2 driven by the Selsy'n motor --93- upon which a mannerthat shall bedes'cribedhereafter a record is obtained showingth'e'v'aria tion of the output of the filter with respect totheimpressed frequency. The Sel'syn 93 isd'riV- en synchronously with theSels'yn 23. I 1

The output of the low-pass filter 89 is e'orn-- nected through theleads'50, 5i to' the excitation windingMl-of the motor 45; 1' Theoperation of the arrangement shown in Fig. In as follows. The oscillatorztl'ie'nergize's' the synchronous motor 26 which, in turn, drives theunbalanced wheel 28 and imparts 'upon the earth through the support 3!corresponding "vizbrations'at a frequency that is determined in a finalanalysis by the setting of 'theshaft25 of the Selsyn motor 22. Theseismic waves'orig limited by the vibratortfl willextend in all'difecrao'rdi-hary" ge" physical stale-prospectin 7 the microseisms level hasa power such that in, frequency bands 100 cycles wide the root meansquare equivalent amplitude is of the order 10" centimeters. Naturally,this magnitude varies from place to place and this figure is considereda fact that is realizable in locations that are reasonably quiet, farfrom ocean surfaces and under conditions of no wind and general calm inthe environment. If we maintain the assumption which has been expressedby numerous workers that this noise is substantially uniformlydistributed, then it is apparent that the wave amplitude decreases asthe band width to which the measuring apparatus responds is reduced. Forexample, if we were to reduce the band width to 1 cycle, the noise wouldbe reduced by a factor of 100 and the noise amplitude would be reducedby a factor of 10, i. e., it then becomes 10- centimeters. If we reducethe band width to /ion of a cycle, the noise amplitude becomes l" and,if we reduce the band width still further, the noise becomes reducedcorrespondingly, and there is no limit to the amount of noise reductionthat can be achieved by reducing the band width.

;[t is apparent that the decrement of the measuring circuit will becomesmaller at the band width is reduced and, consequently, the timerequired for a steady state condition to become established in thecorresponding apparatus increases. It is further found that the processof increasing the measuring apparatus sensitivity with a correspondingincrease in the amount of time required to perform a single measurementcan be carried on indefinitely. This manner of achieving very greatsensitivity in measuring apparatus is used widely in radiationmeasurements. In these measurements (for example, the measurement of theionization current in an ionization chamber used for measuring theintensity of gamma rays) there always is present a certain statisticalfluctuation which increases the noise. This statistical fluctuation canbe reduced more or less indefinitely by increasing the time constant ofthe measuring apparatus. In certain very diflicult readings timeconstants of as long as several hours have been used and in some casesby means of special circuit known as scale circuits effective timeconstants of even longer duration have been obtained. In certain fieldsof geophysical prospecting as for example the radioactivity logging ofoil wells, the use of a long time constant in order to reduce noise isan inherent part of the process without which the apparatus would beinoperative.

It is the purpose of my invention to use some of the principlesdescribed above in order to reduce the noise that heretofore has been abarrier to a great instrument sensitivity. By reducing the noise it willbe possible by the use of my invention to reduce correspondingly theintensity of the seismic wave reflected from lower subsurface beds, and,consequently, the results obtained will provide information regardingthe geological conditions at considerably larger depths.

It is therefore apparent, that the geophone 60 picks up the usefulsignal which is being represented by various waves that are brought intobeing as a result of the periodic excitation of the earth by means ofthe vibrator 28, and the noise caused by the microseisms. The output ofthe geophone 60 is subsequently applied to the amplifier 6| which is ofa conventional design.

It has been found that there is an inherent limit to the amplificationof the amplifier BI and this limit depends upon the width of the band towhich the amplifier is responsive. It is well known that the outputsignal of the geophone 60 that it is desired to amplify and whichrepresents the useful seismic signal together with the microseisms isnot the only signal appearing across the output terminals of theamplifier 61. The output signal of the amplifiers BI is usuallysuperimposed upon the undesired noise signal which depends upon the bandwidth of the frequencies to which the amplifier 6| is responsive.

Under ordinary circumstances the greater is the depth of a reflectingbed the weaker is the reflected seismic signal and, therefore, atsufliciently low depths the reflected seismic signal becomes so weak asto be completely masked by the noise signal resulting from microseisms.Therefore, there is a definite limit to the depths of the reflectinggeological beds that can be measured. It is also apparent that thesignal derived from the geophone should be sufficiently intense as tooverride the noise due to the amplifier and which results from thecombined action of shot effect, thermal agitation, secondary emission,etc.

In order therefore to adapt my arrangement to indicate lower geologicalbeds, it is necessary to take into consideration the microseisms and thethermal noise of the amplifier 6|. The instrument should be designed insuch a manner as to limit the noise due to microseisms and the noise dueto the thermal agitation in the amplifier 6| and to increase the signalto noise ratio.

It is therefore apparent, that across the output terminals of theamplifier Bl we obtain two signals; the signal having the frequency 1which is equal to the frequency imparted to the earth by the vibrator28, and the noise signal which is distributed over a frequency banddetermined by the characteristics of the amplifier SI and of thegeophone 60, the said noise signal being originated by the microseismspresent in the earth and the thermal agitation present in the amplifier6|.

It is the purpose of my invention to eliminate the noise from the outputterminals of the amplifier GI and I am therefore connecting the outputterminals of the amplifier 6! to a variable filter included in thedotted rectangle N10. The variable filter I00 can be adjusted totransmit only the frequency f of the seismic waves originated by thevibrator 28 and to attenuate all the noise frequencies.

It is apparent however that the frequency f is a variable frequency,since in accordance with my invention the impressed seismic frequency fimparted to the earth surface by the vibrator 28 is being continuouslyvaried by means of the controlling element 2| driven by the Selsyn motor22.

Therefore, the tuning of the filter we must be continuously varied andbe always adjusted so that at any particular moment the filter H30should transmit only the frequency f corresponding to the useful seismicsignal originated by vibrator 28 and to attenuate all remainingfrequencies.

In accordance with my invention, the frequency of the seismic wavesgenerated by the vibrator 28 is continuously varied at a very slow speedby slowly turning the handle 2% of the Selsyn 23. By means of anarrangement that shall be described hereafter the mid-frequency of thefilter I00 is made to follow the frequency variation of the vibrator 28and, consequently, the signal to noise ratio at the output terminals ofthe filter Hill? is very large, dependent primarily upon the width ofthe band to which the filter is responsive. The filter that I propose touse is only a small fraction of a cycle wide and very good signal tonoise ratio can be produced.

Consider now the operation of the variable filter I90. As shown in thedrawing, the filter Hill includes the balanced modulator E2 in cascadewith the low pass filter 90. As described in the preceding paragraphs,two signals are produced across the output terminals of the amplifier Siand applied to the input terminals of the balanced modulator 62. Onesignal is the useful seismic signal having the frequency f of thevibrator 28, and the other is the noise signal distributed over asuitable band width in the neighborhood of y and representing themicroseisms on the earth surface picked up by the geophone 6i} and thenoise of the amplifier El. The modulator also receives across its otherinput terminals so a voltage derived from the generator 38. This voltagehas the same frequency as the useful seismic signal applied at the inputterminals '18 of the balanced modulator 62. By means that shall bedescribed hereafter I maintain the input voltage applied at theterminals 88 always in phase with the useful seismic signal applied atthe terminals 18.

It is apparent, that We obtain across the output terminals 82 of themodulator t2, voltages which represent modulation products of the twoinput voltages. One of said input voltages has the frequency f of thevibrator 23 and is applied across the terminals 89. The other inputvoltage contains the useful seismic signal having the frequency f, andthe noise voltage distributed over a frequency band in the neighborhoodof f. It is apparent, that the voltage component in the output of themodulator 62 which results from intermodulating the input voltageapplied across the terminals with the useful seismic signal isrepresented by a direct current. It is also apparent, that themodulation product between the noise signal derived from the inputterminals l8 and the voltage derived from the terminals 89 producesacross the output terminals 82 only A. C. voltage.

As shown in the drawing, the current derived from the output terminalsof the modulator 62 is transmitted through the low pass filter so havinga relatively low limiting frequency determined by the time constant RCof the circuit where R designate the series resistor ill) of the filterand C designates the shunt capacitor iii of the filter. It is thereforeapparent that the filter 953 will transmit the D. C. component of theinter modulation products derived from the terminals 82 and willattenuate the A. C. components of said intermodulation products.

It has been explained above, that the D. C. component of theintermodulation products represents the useful seismic signal detectedby the geophone 86 and that the A. C. components which are attenuated bythe filter to represent the noise due to microseisms and to theamplifier (i I. It is therefore apparent, that the voltage derived fromthe output terminals H2 of the low pass fiiter as representssubstantially the useful seismic signal. This signal is subsequentlyapplied to the recorder 3! wherein it becomes impressed upon the strip92.

The above method is characterized by an extraordinary degree of noiseelimination. The

method. consists essentially in deriving from the leads 4!) a voltagehaving the same frequency and phase as the useful seismic signal derivedfrom the amplifier BI and in producing a modue lation product betweenthe useful seismic signal to be measured andderived from the amplifierBI and the voltage derived from the leads ll). This modulation productwill be a direct current, since the frequency and phase derived from theleads 4 0 is equal exactly to the frequency and phase of the usefulseismic signal derived from the ainplifier 6|. At the same time itbecomes apparent that the noise frequencies accompanying the usefulseismic signal are represented by modulation products which arealternating currents and these alternating currents are attenuated bythe low pass filter 9a.

Consider a component of the noise spectrum obtained from the amplifier6i and having a frequency f Let the modulation product derived from themodulator 62 and corresponding to the frequency f be represented byan'alternating current having a frequency f It is apparent, that thesmaller is the difference between the frequency f and the frequency f ofthe useful seismic signal the smaller willbe the frequency i. e., forthose frequency components of the noise voltage which are very close tothe signal frequency f the corresponding modulation products arerepresented by A. C. currents of very low frequencies. On the otherhand, the farther apart are the frequency components of the noisespectrum from the frequency f of the useful signal, the higher are thefrequencies of the-corresponding modulation products. It is the purposeof my invention to transmit only an extremely narrow band of noisefrequencieslying in the immediate neighborhood of the useful seismicsignal frequency f and to attenuate completely noise frequencies whichare farther apart from f in the frequency spectrum. I accomplish thispurpose by impressing the output of the modu lator 62 upon the low passfilter 90. The low pass filter is adapted to transmit the D. C. currentcorresponding to the signal 1 and onlya very narrow band of lowfrequency currents cor.- responding to a very narrow band of noisefrequencies located in the immediate neighborhood of the useful seismicsignal frequency f.

Let the 10W pass filter 90 be designated so as to transmit the D. C.current and the frequency band comprised between the frequency zero anda maximum frequency fmax where the value fmax is relatively small. It isapparent, that the frequency applied to the input of the balancedmodulator 62 and corresponding to the frequency zero in the output, isthe frequency f of the useful seismic signal. and the input frequency ofthe balanced modulator corresponding to the output frequency fmax is thefrequency "f-l-fmax or .f-"fmax. This can be easily verified if we takeinto consideration that the output frequency of the balanced modulatorrespresents a modulation product between the input frequencies, i. e.,when the input frequencies are i and f-i-fmax the output frequency isfmax and when the input frequenciesare f and f--fmax the outputfrequency is also 'Jmax. Therefore, the frequency band transmittedthrough the whole filtering system I00 including the balanced modulator62 and the low pass filter 90 is limited by the frequencies f-I-fmax andf-fmax and the width of of said pass band is Zfmax. Consequently, thewhole filtering system I including the balanced modulator and the lowpass filter as a whole behaves as an extremely narrow band pass filterthe width of which is twice that of the low pass filter. The width ofthe low pass filter 90 can be decreased almost indefinitely by the useof a circuit consisting of the resistor H0 and the condenser III, as ithas been done in case of the filter 90. Such a circuit can be made tohave a time constant of several days which corresponds to a band widthof the order of 10* C. P. S. Using an arrangement as described, it ispossible to measure voltages of known frequency in the presense of alarge amount of noise and good results have been obtained when themagnitude of the total noise is several times the magnitude of thevoltage representing the signal.

In practice the low pass filter 90 as represented by the condenser IIIand the resistor IIO may be replaced by a conventional low pass filteras for example of a constant K type. However, in the embodiment of Fig.2 I have chosen a resistance condenser circuit because of the greatflexibility of design. A condenser III of 4 microfarads and a resistorIIO of 250,000 ohms will provide a substantially uniform response fromthe frequency zero up to the frequencies of 1 cycle per second and zeroresponse for the frequencies higher than 1 cycle per second. It isapparent that for the above value of the condenser III and of theresistor IIO the whole filtering system I00 including the balancedmodulator and the low pass filter as a Whole behaves as a band passfilter having a band width of 2 cycles per second.

It is also apparent that when the condenser III has the value of 4microfarads and the resistor I I0 the value of 2.5)( ohms, then thefiltering system I00 behaves itself as a band pass filter having theband width of 0.2 cycle per second. Or, if the condenser I I I has thevalue of 4 microfarads and the resistor IIO has the value of 2.5 10ohms, then the corresponding band width of the filter I00 will be 0.0002cycle per second. Or, if the condenser II I has the value of 4microfarads and the resistor IIO has the value of 2.5 10 ohms, then thecorresponding band width of the filter I00 will be 0.000002 cycle persecond.

The output of the low pass filter 90 is connected to a. recordinggalvanometer 9| which comprises a field magnet I20, and a movable coilI2l which is well damped. A mirror I22 is carried by the coil I2I andlight from an incandescent lamp I23 is projected upon the mirror I22 forreflection upon the light sensitive strip of paper 92. A suitable meansis provided such as the Selsyn motor 93 for moving the light sensitivepaper synchronously with the Selsyn v23 past the light spot reflected bymirror I22. The mirror I22 directs the beam of light upon the strip 92and is adapted to modify the light in accordance with the magnitude ofthe signal derived from the filter The record obtained upon the movablestrip 92 represents the earth characteristics with respect to twocoordinates and has form of a graph substantially of the type shown inFig. 3. The longitudinal coordinate parallel to the length of the strip92 is the frequency coordinate because the strip 92 is moved lengthwisesynchronously with the Selsyn 23. To each position of the handle 24 ofthe Selsyn 23 corresponds a definite frequency f imparted to the earthby the vibrator 28, and by varying said position the frequency f isvaried. In a similar manner, to each position of the handle 23corresponds a definite position of the strip 92 and by varying theposition of the handle the position of the strip is varied.Consequently, the strip 92 is moved in a definite time relationship tothe variation of the imparted frequency f and at any instant theposition of the strip 92 corresponds to a definite value of thefrequency f. The strip 92 receives the impression of the light beamreflected by the mirror I22, the said light beam being movable in adirection perpendicular to the direction of motion of the strip 92, thesaid perpendicular direction representing the output of the filter I00,i. e., the useful seismic signal picked up by the geophone 60 andoriginated by the vibrator 28. Consequently, the graph obtained upon thestrip 92 and substantially as shown in Fig. 3 represents the behavior ofthe earth with respect to two coordinates, one of said coordinatesrepresenting the frequency f of the seismic wave imparted to the earthby means of the vibrator 28, the said frequency being varied within adetermined range, and the ordinates represent the corresponding valuesof useful seismic signals picked up by the geophone 60 and correspondingto said frequencies.

It is apparent therefore, that I have provided the necessary apparatusfor seismic exploration by means of periodic waves and that because ofthe extreme sharpness of the filtering apparatus enormous sensitivityhas been achieved while still maintaining a satisfactory signal to noiseratio. Consequently, the curve produced by the recorder 9| is a curve inwhich the response versus frequency characteristics of the earthintervening between the vibrator 28 and the geophone 60 is drawn. Such acharacteristic has the well known peaks and valleys in it, which areproduced by various reflecting and retracting horizons within theexplored region.

It has been stated in the preceding paragraphs that in order to separatethe useful seismic signal having the frequency I from the noise signal Iam adjusting automatically the phase of the input voltage applied acrossthe terminals of the modulator 62 in such a manner as to make the phaseof said input voltage coincide with the phase of the useful seismicsignal derived from the amplifier 6|.

The phase of the voltage derived from the leads 40 and applied acrossthe input terminals 80 of the modulator 62 is being automaticallyadjusted by means of the modulator 65 in the following manner:

The voltage derived from the geoph'one 60 is applied to the modulator 65through the derivator 63. The derivator 63 because of the nature of itsperformance in the case of sinusoidal voltages produces a voltage theoutput of which is out of phase with the voltage at its input,consequently, the voltage supplied to the modulator 65 is always 90 outof phase with the voltage supplied to the modulator 52. This conditionis regularly followed for any Value of the frequency of the inputvoltage derived from geophane 60. If we give our attention to thebehavior of the modulator 65 it will be observed that across theterminals 15a, 151) there will be produced a D. 0. voltage the magnitudeof which is proportional to the product of the voltage supplied by thederivator 63 and the voltage supplied by the generator 38. Furthermore,as has been described above the voltage appearing across the outputterminals 15a, 15b is positive when the voltage across the inputterminals 10 is in phase with the voltage across the input terminals Hand is negative when this phase relationship is reversed. Furthermore,it is zero when the phase relationship is 90. Assume now for examplethat the phase relationship is such that the modulator output produces aD. C. voltage such that the output terminal 150, is positive withrespect to the output terminal 15b. This voltage is transmitted throughthe low pass filter 89 and becomes subsequently impressed across theexcitation winding 48 of the motor 45 in such a manner that the motor 45actuates the differential gear 34 in a given direction and shifts thephase of the voltage produced by the generator 38. This phase graduallyshifts until the 90 relationship between the phase of the voltages atthe input terminals II and the input terminals 16 is achieved. It can beseen that the action of the circuit is such that the phase across theinput terminals H will always be automatically maintained 90 out ofphase with the voltage across the input terminals 10. This phase controlis continuous and automatic and any external effeet which attempts tobring about a disturbance of this phase relationship is immediatelycounteracted by the action of the automatic phase control circuit.Consequently, it is important to remember that as long as the automaticphase control circuit is in operation the phase between the voltages atthe input terminals II is always exactly 90 with respect to phase of thevoltage across the input terminals 10.

Consider now the modulator 62. As has been stated previously because ofthe action of the d'erivat-or 63 the phase of the voltage appearingacross the input terminals 19 is 90 out of phase with respect to thevoltage appearing across the input terminals 18. Consequently, thevoltage appearing across the input terminals 18 is'always either exactlyin phase or exactly out of phase with the voltage across the inputterminals 80, i. e., the two voltages are either exactly in phase orexactly out. of phase depending upon the initial conditions.Furthermore, it is apparent that once the circuit has been set intooperation the phase of the voltage appearing across the input terminals8!) will lock with the phase of the voltage across the input terminalsi6 and will remain locked as long as the automatic phase control circuitis in operation. Consequently, the suitable ultimate conditions arechosen. The voltages supplied to the modulator 62 are always exa'ctly inphase and the combination of the modulator 62 and low pass filter 9 actsas a band pass filter having an extremely narrow response band.Furthermore, the mid frequency of this filter will automatically followthe frequency of the oscillator 20.

It is therefore apparent, that my method consists essentially inproducing by means of the lgeneratortt avoltagehaving the frequency 1equal to the frequency of the useful seismic signal picked up by thegeophone 60 and in phase with respect to the said signal. Assumetherefore that the conditions are such that the frequency f of thesignal derived from the generator 38 is equal to the frequency f of theuseful seismic signal derived from the amplifier GI and that the phaseof the signal derived from the generator 38 coincides with the phase ofthe useful seismic signal. Un- 'der these conditions we obtain acrossthe output terminals of the modulator 62 two resultant voltages one ofthe said resultant voltages reprc senting the useful seismic signal andthe other resultant voltage representing the noise signal. The noisesignal becomes subsequently eliminated by the low pass filter 9B, andconsequently, across the output terminals of said filter we obtain theuseful seismic signal.

It is apparent that the band width occupied by the useful seismic signalis zero only when the frequency of the impressed seismic waves'originated by the vibrator 28 does not vary with time. However, underordinary conditions the impressed frequency of seismic waves varies and,consequently, the frequency f of the useful signal derived from theamplifier 6| varies according to a certain rate. Therefore, the usefulseismic signal applied across the terminals 73 0ccupies a certain bandwidth which depends upon the said rate. Consequently, the filter IllElmust admit the band width occupied by the said varying useful seismicsignal and at the same time it admits unavoidably the undesirable noisesignal which is contained within said band width. Therefore, when thefrequency of the impressed seismic waves varies rapidly, the band widthrepresenting the useful seismic signal is. increased and the systemresponsive to the useful seismic signal must necessarily admit a largeramount of noise. Under ordinary conditions the rate of change of theimpressed seismic waves originated by the vibrator 28 does not increasebeyond a determined limit and, therefore, the useful seismic signal iscontained within a band of a determined and a relatively small wldth.-As shown in the drawing, the current derived from the output terminalsof the modulator 62is transmitted through the low pass filter having arelatively low limit frequency determined by the time constant RC of thecircuit Where R designates the series resistor H0 of the filter and Cdesignates the shunt capacitor ill of thefilter. If the time constant ofthe circuit RC is designed so that the charge in the condenser C canjustfollow the variations of the frequency of the vibrator 2'8, but isincapable of following faster variations, then the circuit is capable ofmeasuring the useful seismic signal to the limit of measurability. i

It can therefore be readily appreciated the rate at which frequencycontrolling element 2i is varied by means of the handle 26 must be lowerthan a certain predetermined value. It is apparent that an increase inthe variation of frequency of the vibrator 25 broadens the band width ofthe useful seismic signal and that the band width is zero only when thefrequency of the vibrator 28 is constant, and the band width is verysmall only when the rate of change of frequency is very small.Consequently, whenever it is desired to measure a signal that has alarge rate of change of frequency one forcibly admits a larger amount ofthe noise.

With further reference to Figure 2, I have provided an additionalcircuit including a rheostat i353. This rheostat is of the type in whichthere is a stationary circular member I3! of a relatively highresistance and a movable member I32 having one terminal. 33 connected tothe shaft 52 and the other terminal I34 adapted to slide upon thecircular member If. This stationary The movable arm I32 is se- 1 curedto the shaft 42 and when the shaft 42 rotates the movable arm E32rotates with it and slides along the circumference of the stationarymember of the rheostat I38. A wire I is connected to the movable arm I32and another wire MI is connected to the center tap of the battery I31.These two wires energize a recorder I 56. The recorder I comprises afield magnet I5I, and a movable coil I52. A mirror I53 is carried by thecoil I52 and light from an incandescent lamp I is projected upon themirror I53 for reflection upon a light sensitive strip of paper I60. Asuitable means is provided such as a Selsyn motor I6! for moving thelight sensitive paper synchronously with the Selsyn 23 past the lightspot reflected by the mirror I53. The mirror I53 directs the beam oflight upon the strip I and is adapted to modify the light in accordancewith the magnitude of the signal derived from the wires I40 and MI.

It is apparent that the voltage across the wires I40 and MI indicates atany moment the phase difiference between the input of the motor 26 andthe output of the generator 68. Sinc the input of the motor 26 is inphase with the generated seismic waves and the output of the generator38 is maintained to be in phase with the seismic vibrations received bythe geophone 60, it is apparent that the voltage across the Wires I40,MI is indicative of the phase difference between the seismic wavesgenerated by the vibrator 28 and the seismic wave received by thegeophone 60. The Selsyn motor I6I drives the strip I60 synchronouslywith the Selsyn motor 23 and, consequently, the graph produced on thestrip I60 indicates the phase versus frequenc characteristic of thereceived seismic waves. The graph obtained by means of the recorder I58is an important aid to the interpretation of the graph obtained by meansof the recorder 9I because, as is well known, any system can beinvestigated electrically either by means of transient or by means ofsteady state voltages and the information derived by means of one methodcan be translated into information derived by means of the other method.In order to reconstruct the transient characteristics of a system it isnecessary to know the frequency characteristics and the phasecharacteristic. The circuit shown in Figure 2 provides both thesecharacteristics.

With further reference to Fig. 2, numeral I13 indicates a worm andnumeral I1I indicates a gear meshing with said worm. Numeral I12indicates a shaft connected to the gear "I and driving a movable arm I13of a rheostat I1 5. The rheostat I14 comprises a stationar circularmember I15 which is connected across a battery I80 in a manner such thatacross the leads I85, I86 there appears a voltage which is a function ofthe angular position of the shaft 42. This circuit serves to eliminatethe ambiguity that is present in the voltage supplied over the wiresI40, I4I. It is apparent that after the shaft 42 has made a number ofrevolutions it is possible to determine from the voltage supplied bywires I85, I86 whether all these revolutions occurred in the samedirection or whether some of these revolutions occurred in the oppositedirection. The gear ratio between worm I10 and pinion I1I is such thatthe shaft I12 in practice will never execute more than one revolution.And consequently the voltage supplied over wires I85, I86 serves toeliminate the possible ambiguity of the circuit comprising the rheostatI30. The wires I85, I86 go to a recorder I90.

The recorder I90 comprises a field magnet ISI,

and a movable coil I92. A mirror I93 is carried by the coil I92 and froman incandescent lamp I95 is projected upon the mirror I93 for reflectionupon a light sensitive strip of paper 200. A suitable means is provided,such as a Selsyn motor 20I for moving the light sensitive papersynchronously with the Selsyn 23 past the light spot reflected by themirror I93. The mirror I93 directs the beam of light upon the strip 200and is adapted to modify the light in accordance with the magnitude ofthe voltage derived from the leads I85 and I86.

Fig. 4 shows a modification of part of the circuit illustrated in Fig.2. In this arrangement the automatic phase control circuit is eliminatedand the modulator 65 does not operate. The phase adjustment is providedmanually by means of a knob 2I0. By adjusting this knob it is possibleto vary the conditions in the differential gear 34 so that the voltageapplied to the motor 26 and the voltage obtained from the generator 38can be set at any predetermined value and left fixed at that value whilethe medium is being explored. Under these conditions the phase of thevoltages supplied to the input terminals 18 and is no longer fixed butvaries in response to the conditions within the explored medium.Consequently the output of the modulator 62 consists of a D. C. voltage,the polarity of which changes as the phase of the earth vibrationspicked up by the geophone 60 changes. The characteristic produced by therecorder 9| is, therefore, similar to the characteristic producedpreviously but instead of being an undirectional curve it is a curvethat oscillates from positive to negative values every time the phase ofthe currents supplied by the geophone 60 goes through a reversal.

Consider now Fig. 5 which represents diagrammatically a double balancedmodulator designated on Fig. 2 by blocks 62 and 65. Let the voltageapplied across the input terminals 241a, 2411), be designated as E sin21rft and and voltage applied across the terminals 215a, 2151) bedesignated as E sin (21rft+0). It can be shown that when 0%0 theD.C.component of thevoltage across the output terminals 216a, 2161) iszero. It has been stated above that a noise signal uniformly distributedover the frequency range of a determined width is applied across theinput terminals 241a, 2411). It is then apparent that if we integratethe contribution due to all the noise frequencies over the entire bandfor all the frequencies with the exception of the frequency component 1corresponding to the useful seismic signal, then the D. C. voltageacross the output terminals 216a, 2181) will be zero. It is alsoapparent that the noise component correspondin to the frequency isinfinitesimal. Consequently, the total noise signal will not contributeat all to the D. C. component of the voltage across the output terminals216a, 21612. Therefore a D. C. component will appear across the outputterminals 216a, 2161) only if there is a useful seismic signal impressedacross the input terminals 241a, 241D and if the frequency f of thissignal is equal to the frequency ,f of the voltage applied across theterminals 215a, 215?).

The circuit illustrated in Fig. 5 comprises a bridge circuit consistingof four rectifiers 30I, 302, 303, 304, each of the said rectifiersconstituting a separate arm of the bridge circuit and arranged so thatthe current can flow only in an anticlockwise direction. The uppercorner of the bridge 305 and the lower corner of the bridge 306 arerespectively connected to the input terminals 241a, 2412) and are alsoconnected one to another by means of equal resistances 301 and 308 inseries. The other corners of the bridge 309, 310 are respectivelyconnected to the output terminals 216a, 21% and are also connected oneto another by a pair of equal resistances 3 and 3|{2 in series. Theother input terminals 215a, 2-15 of the balanced modulator arerespectively con nected to the point 3 I3 connecting the resistances301, 308 and. to the point 314 connecting the resistances 3|2, 3|

With the circuit as described, current derived from the terminals 241a,2411 may flow either through the rectifiers 302, 303' or through therectifiers 304, 30| depending upon its direction but it can never flowthrough all the four recti fiers at the same time, since the rectifiers302-, 303 on one hand and the rectifiers 30 3', 301 on the other handare arranged to flow in opposite directions.

Suppose now for purposes of illustration that the voltage derived fromthe terminals 215a,. 2155 and the voltage derived from the terminals241a, 2472) are simultaneously applied, and suppose that both voltagesare in phase, 1. e., the terminal 241a becomes positive as compared tothe terminal 2 11b and at the same time the terminal 2151: becomespositive as compared to the terminal 21%. Then one part of the currenttends to flow from the terminal 215a. to the terminal SH! and throughthe resistor 301 to the terminal 305' and then through the rectifier 302and through the resistor 3| I back to the terminal 21%. The other partof the current tends to flow fromth'e terminal 215a to the terminal 3 i3and throu'gh the resistor 308 back to the terminal 306 and through" therectifier 303 and through the resistor 3 l'2back to the terminal 275?).The currents flowing through the resistors 3| I, 3|2 are equal and ofopposite directions.

It is apparent that under the conditions described in the precedingparagraph the polarity of the terminals 335', 308 will be positivewithrespect to' the polarity of the terminals 3093 3-'|0. Consequently,positive voltages are applied to rectifiers 302, 304. Therefore theserectifiers will lose their ability of rectifying currents, and willallow currents to traverse them in both directions. At the same timenegative voltages are applied to rectifiers 30f and 303. Consequently,thereotifiers 3!, 303 will retain their rectifying ability and willblock currents attempting to traverse them in the negative direction.Therefore the rectifiers 302 and 304 are conductive in both di-'rections and consequently, when a signal voltage is being developedacross the terminals 2410,,

24% we find that a current tends to pass from.

the terminals 24101 to the terminal 305 and thenthrough the rectifier302 through the resistors 3| and 3|2 to the terminal 3|0, then. throughthe rectifier 304 back to the terminal 24-111. This current superposesitself upon the current which is already flowing through the resistors3H and 3|2 and consequently the resultant current passing through theresistor 3| becomes larger than the current passing through the resistor31-2. Consequently, the balancing that existed before is offset becausethere is a situation where the current flow through the resistor 3| isincreased as compared to the current flow through the resistor 3|2. Thusthe voltage drop across the resistor 3 becomes greater and a positiveoverall voltage is developed across the terminals. 216a, 21%. It is thusapparent that theexistence of the lower bed located at a depth (12.

18' the two Voltages, in phase, one applied to the terminals21511,.215?) and the other applied to the terminals 241a, 2411) createsa voltage across terminals 276a, 21% of a definite polarity. y

It can be shown that if the polarity of the first input voltage wouldreverse with respect to the second input Voltage, i. e., if we supposethat the terminal 2 15a becomes positive as compared to the terminal2151; and the terminal 241a becomes negative ascompared to the terminal241?) the current flow through the resistor 3|2 isingceasedz-asicomparedto the current flow through the resistor; 3H. Thenthe voltage drop across. the resistor 3%: becomes larger and the overallVQB}&-g;;dBV1013dacross the output terminals- Zifia, 21532; has apolarity opposite to the case d'escribed above. 7

It can-also be shown that inanintermediate situationwherethe signalvoltage derived. from. the. input terminals 2 15a, 2155 is displacedbydegrees with respect tothe voltage derived from the inputterminals211a,, 2415 their the D. C. voltageoutput from the ring: modulator iszero.

In general, it we designate thevclt'age applied across the terminals2510., 2471i as Ei sin 211315 and the voltage applied. across theterminals 215a,. 2155 asv Eel sir-i (2'5rff+Q) then the voltage developed! a'c'ro ssthe output terminals 276a, 2161) can be represented asEacos 0.

consider new. again Fig. 2 in which there is shown alsodiagrammaticallythe earth cross sec t'ion below the source'of lsei'smicj waves 28f and the geophor'ie'j 601'; The numeralflfi 007indicates the upper layercomposing-the first thousand feet or so of theearths crust. Beneath thisthere is shown ahard underlying stratum 60 Itis apparent that asthe flywheel 30 revolves, there will v be. a.verticalcom-ponent of. force directed towardthe earth. This is indicatedby the eduationi F'="W"-|-C'sin!2'1rfit (1) Where W is thenormal forcedue to the wei'ght'-of-" the device, f is the impressed frequency and Cis the amplitude of the impressedvibratory motion. It is apparent thatthe value of the frequency is; determinedv by the. condenser. 2|, 1...e., by the instantaneous. position of'ith'e shaft of the selfsynchronousmotor 23. Wehave assumed; that the speed of rotation ofth-efielsynmotorsfi and 23fisextreniely slowcom'p aredto the speed of the motori'fiTherefore in order to consider the effects oftheimpressedfrequencyj-whi-ch is determined by the rotational speedof'themotor 2 B we shall assume that the shaft'of' the'Selsyn motor 22 isstationary. V

The"displ'acement of the'" ea'rths surface then will be:

neglecting theeffect of the: weight which: is com-- st antt' TheconstantId eXpre'ssesthe' proportion ality ofrthetwosidesontheequation.

As: already stated; the functioning or the wheel 30 will alternatelydepress'andzraisesthei surface: otfthefearth... The waves resulting fromthenrotioni. ofthe earths surface will extend: in all: directions withsome type: of spherical: form. We have assumed: that: the geoph'one 60is located:'. at the: distance:- d1; from thevibrator 2-8,...the"saidgdistan-ce-r being, measured along" the ground: surface. Some? waveswill. propagate on the sur:- face cf-the earthdhectl-y from the'vibrator28-. to: the-geophone G0,. some will penetrate; below the roun -i a t-bee e t d: r sh t e u ac 590- f The surface wave travels a shorterdistance from the vibrator 28 to the geophone 60 than any reflected,diffracted, or refracted wave. The direct surface wave is indicated bythe numeral 6H) and the downwardly traveling indirect wave which becomessubsequently diffracted and returned to the ground surface is indicatedby the numeral 6| l. Another wave designated by the numeral 6|2 travelsdownward to the subsurface 590, then it becomes reflected and returnedto the geophone [50.

It is apparent that the waves H0, 6 and H2 superpose themselves at thepoint at which the geophone 60 is located and that the geophone motionwill represent a resultant wave which represents the interference effectdue to the waves 6H], 6H, CH2.

In order to facilitate the explanation of the method we shall assumeidealized and simplified conditions under which only two waves, i. e.,the waves Bill and 6 are present and we shall consider the interferenceeffect due to these waves. It is apparent that the maxima or minimaresulting from the interference depend on the difference in length ofpaths traversed by the waves Gill and BI! respectively. This is furtherdependent on the depth and the slope of the stratum 60!. As shown inFig. 2 the length of the direct path Bill is the length of the segmentAB=d1 and the length of the indirect path 6| I is the sum of thesegments AC, CD and DB and is equal to 2d2+d1 since AC=DB=d2 andAB=CD=d1 In general, the time t is equal to distance (1, divided by thepropagation speed 2):

Therefore if we assume a horizontal upper and lower surface of the layer600, a constant frequency of the vibrator 28, and neglect any phasediscontinuity, the difierence in time (h) between the two paths 6H) and6H will become:

Where in, the phase speed in the upper stratum 600 w, the phase speed inthe lower stratum 6M It is therefore to be seen that the Formula 4 takesinto account the fact that the velocity changes with the depth and withthe different types of structures. Consequently, it will be necessary toexperiment from known depths to determine the terms 01 and 02.

It is therefore apparent that the two waves BIO and 6H produce aresultant wave which can be expressed as follows:

Additional terms may be added for additional waves such as the wave H2.The terms k1 and 702 are proportionality factors, which depend upon theelasticity and absorption characteristics of the earths strata.

It is therefore apparent from the Equation that the geophone 60 issubjected to a sinusoidal motion having the impressed frequency f and anamplitude which is determined by the time difference t, between the twocomponents of the expression (5). The amplitude of the geophone outputas defined by the expression (5) constitutes the useful seismic signalreferred to above and is being impressed upon the photographic strip ofpaper 92 in a manner explained hereinbefore.

Consider now an instant later when the Selsyn motor 23 has performed avery small angular displacement. Then a new and slightly differentfrequency f is being generated by the vibrator 28. By referring now tothe expression (5) we can readily realize that the interfering waves 6)and 6H striking the geophone 60 will be characterized by slightlydifferent values of f and t1. Consequently, the useful seismic signalpicked up by the geophone 60 will have a slightly different value. Atthe same time the Selsyn 93 has performed a small angular rotation andhas displaced the paper strip 92 which receives by means of the sourceof light I23 and the mirror I22 an indication of the new useful seismicsignal derived from the geophone 60.

It is apparent that by continuously varying the displacement of theself-synchronous motors 22 and 93 a trace is being produced upon thestrip 92, this trace being similar to the graph of Fig. 3. Thelongitudinal displacements of the strip 92 represent the frequencies ofthe impressed waves and the transversal deflections of the beam of lightrepresent the useful seismic signals derived from the geophone 60.Consequently it is apparent that the curve recorded upon the strip 92represents the frequency-amplitude characteristic of the variousimpressed waves detected by the geophone 60 and due to the vibrator 28.

It is apparent that in a homogeneous medium the vibration amplitudedecreases inversely with distance for space waves, and inversely withthe square of the distance for surface waves. Further, there is anexponential decrease due to absorption. In a stratified medium such asshown in Fig. 2 the directly transmitted waves BIO interfere with thereflected and refracted waves because of their path and their phasedifference. The amplitude frequency curve such as shown in Fig. 3 istherefore not uniform as in a homogeneous medium, but shows a series ofmaxima or minima, the said maxima being designated by the points A1 B1,C1, D1, and E1 in Fig. 3.

It is also apparent from the preceding paragraphs that since the phasedifference between the surface wave and the underlayer wave is thereforea maximum in amplitude occurs when and a minimum occurs when 1 ii.:|:21rfl v1 +d1 )-(2z;;1)1r s successive maxima is equal to the ratio oftwo successive numbers or The condition corresponding to the frequenciesf defined by the expression ('7) is known as resonance. Since thereturning indirect wave 6| 1 is in phase and is of the same frequency asthe direct surface wave H0, it need now only oversome the viscosit andnot the elastieitr of: th earth materials, and the resulting; increaseof amplitude may be greatly amplified. Resonance is to be considered thestrongest indication of reflection or refraction from subterraneanstrata. Various resonance points resulting from the interf erence ofwaves Gift and 6H are designed as A1 B1, C1, D1, and E1 in the diagramof Fig. 3.

Let f1 be the abscissa corresponding to the lowest resonance point A1.Then by substituting i=1: in the expression (-1) it becomes apparent 12d2 L m wherefrom J1 l int g/*1 an:

It is apparent that eh, m, in can be measured and that f1 can also bemeasured from the graph of Fig. 3-. Consequently, by utilizing the datasupplied. by the frequency amplitude graph of Fig. 3 the Formula 12allows us to determine the unknown depth d2 of the underlying geologicalhorizon.

The purpose of the invention, of course, is to find changes in elevationof a particular structure, or structures, lying near the strata supposedto contain oil. An appropriate number of readings at intervals over agiven territory will be sufficient to map the subterranean contours.

I claim:

1. Method of subsurface seismic surveying which com-prises generating aperiodic disturb ance in the earth and varying the frequency of saiddisturbance in accordance with a predetermined function, receivi-n-g theresultant seismic waves travelling through the earth at a point removedfrom the source of said disturbance, transforming said received seismicwaves into corresponding electrical currents, selectively receiving saidcurrents and varying the selectivity of said reception simultaneouslywith the variation of the frequency of said disturbance, the variationof selectivity of said reception being effected in accordance with saidpredetermined function, and recording said selectively received waves.

2. Method of subsurface seismic surveying which comprises generating aperiodic disturbance of determined frequency in the earth, receiving theseismic waves caused by said disturbance at a point removed from thesource of said disturbance, transforming said received seismic wavesinto corresponding electrical currents, selectively receiving acomponent of said currents having the same frequency as saiddisturbance, simultaneously varying the selectivity of said receptionand the frequency of said disturbance, whereby the frequency of saidselected component follows th frequency of said disturbance in such amanner that at any selected instant the frequency of said selectedcomponent is equal to the frequency of said disturbance, and producing agraph representing the variation of the magnitude of said component withthe varying frequency of said disturbance.

3. Apparatus for seismic surveying comprising means positioned at aselected location with reference to the earth for generating a periodicdisturbance in the earth, a control element connected to said means forvarying in a determined manner the frequency of said disturbance,

means conveniently distant from. said location for receiving seisznicwaves caused bysaid disturbance-and transforming said waves intocorresponding electrical variations, a selective. net.- work connectedto said receiving means for selectively receiving said variations, andmeansconnected-to said controlling element for varying the selectivityof said network simultaneously, with and in the same manner as thevariation of: the frequency of said disturbance, whereby the. frequencyselected by said network is at any instant equal' to the frequency ofsaid disturbance, and a recorder connected to said network for recordingthe output. of said network.

4. An arrangement for seismic surveying comprising a generator placedata convenient. location with reference to the earth for imparting afrequency modulated seismic waye: having predetermined amplitudecharacteristic into: the earth, a geophone cpnv-eni'ently distant fromsaid generator for receiving a portion of: said: frequency modulatedwaves: after said: portion has been influenced by the-travel intheea-rth; and for translating said wave into a. corresponding ire;-q-uenc-y modulated current; means for producing: a signal representingthe modulating com-ponent; expressing the frequency variation of saidwave, means connected to said receiver for producing another signalrepresenting: the amplitudeof: said current and means:v responsive tosaid! SignalJand to saidother signal for producing a resultant signals5'-. arrangement for seismic prospecting comprising a generatorpositioned at a. selected location with respect to the cart-his.surface; for imparting anenergy wave of a determined freequenc-yinto'the earth, thereby causing said. wave to traverse a portion of: theearth, a control element connected to said generator for: varying thefrequencyof said Waves, a geophone'; con ven-i'ently distant from saidlocation for receiv ing seismic vibrations caused by said' energywaveandfor producing a current representing said vibrations, said currenthaving a significant component originated by said generator and havingfrequency following the frequency of said generator and neighboringnon-significant frequency components representing the disturbancespresent in the earth, means for producing a current of known magnitudeand of frequency following the frequency of the generator and equal atall times to the frequency of the generator, a modulator responsive tosaid current and to the output of said source for producing modulationproducts, said modulation products having components of variousfrequencies and including a useful D. C. component, an electric filterconnected to said modulator for selectively transmitting said D. C.component and for attenuating the remaining A. C. components, and anindicator connected to said filter for providing an index of its output,said index representing the magnitude of said significant frequencycomponents.

6. An arrangement for seismic prospecting comprising a generatorpositioned at a selected location with respect to the earth's surfacefor imparting an energy wave of varying frequency into the earth,thereby causing said wave to traverse a portion of the earth, a geophoneconveniently distant from said location for receiving seismic vibrationscaused by said energy wave and for producing an electrical currentrepresenting the magnitude of said vibrations, means responsive to theimparted and received waves for producing a first signal indicating aphase relationship therebetween, means for producing a second signalrepresenting the frequency variation of said waves, and means responsiveto said first and second signal for producing a re- .sultant signal.

7. An arrangement for studying the vibrations in a given medium,comprising a detector placed at a convenient location with reference tosaid medium for translating said vibrations into electrical currents, afilter connected to said detector for selectively transmitting a portionof said currents, a control element connected to said filter for varyingthe selectivity thereof, a recorder connected to the output of saidfilter, and a means operatively connected to said recorder and to saidcontrol element for operating said recorder and simultaneously varyingthe selectivity of said filter.

8. A method of measuring a significant seismic signal of a knownfrequency, the said signal being accompanied by microseisms distributedover the frequencies neighboring said known frequency, comprising thestep of translating said seismic signal and said microseisms into anelectrical current having a frequency component corresponding to thesignificant seismic signal and neighboring frequency componentscorresponding to microseisms, the step of producing a reference currenthaving the frequency of said significant seismic signal, the step ofintermodulating said electrical current with said reference currentthereby producing modulation products the D. C. component of whichcorresponds to said useful seismic signal and the A. C. components ofwhich correspond to said microseisms, the step of selectively receivingsubstantially said D. 0. component by simultaneously attenuating asubstantial contribution of said A. C. component, and the step ofmeasuring said D. C. component as an index of the magnitude of saidsignificant seismic signal.

SERGE A. SCHERBATSKOY.

24 REFERENCES CITED The following references are of record in the fileof this patent:

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